How to connect parts of a model to the rig?
There are two ways:
If a piece is a stand alone object:
select the object, shift select the rig, enter pose mode, select the relevant bone, press Ctrl P - Bone).
Repeat for all the objects.
If some different pieces are contained in the same object, you can separate them (Press P in edit mode) and use the first method, OR you can use the armature deform: Select the mesh, shift select the rig, press Ctrl P - &quot;With empty groups&quot;.
Then in edit mode select all vertices of a piece (use L and Ctrl L for fast selections), select the relevant vertex group and click assign under the vertex groups list.
As soon as some vertices are assigned to one vertex group only, they will move with the relevant bone exactly, undeformed, no matter which is the value of the weight.